Journal of Conference Abstracts

Recovering the Earth Magnetic Field from its Non-linear Surface Data

Andrei Khokhlov (khokhlov@mitp.rssi.ru)¹, Gauthier Hulot (ghulot@ipgp.jussieu.fr)² & Jean Louis Le Mouel (lemouel@pgp.jussieu.fr)²

¹79, bld.2 Warshavskoe shosse, IEPT RAS, 113556 Moscow, Russia, 113556, Russia

²IPGP, 4, pl.Jussieu, Tour 24, Paris, Cedex 05, France, 75252, France

The main magnetic field is generated within the Earth core and may be described outside the core as potential field with harmonic potential dying at infinity. As a result simultaneous knowledge of this field everywhere at the Earth's surface provides enough information for maps of the field everywhere above the core. In practice however there are two situations of non-vectorial surface data: pure directional data arises from paleomagnetic measurements and intensity only data collected from early satellite observations. The relevant mathematical problem is to establish the conditions when recovering process is unique in appropriate sense (for instance directional case up to a constant multiplier). In the present time we are able to establish reasonable conditions and prove the uniqueness of corresponding directional and intensity problems.

The first Result claims, that if it is known that vectorial geomagnetic field has only two poles (South and North magnetic poles) than vectorial field can be recovered within a constant multiplier in a unique way from its directional data gathered at the Earth's surface.

The second Result claims that if intensity data for geomagnetic field is known with certain precision at the Earth's surface and also (epsilon) -vicinity of the magnetic equator is known (i.e. set of points, where normal component of the magnetic vector does not exceed small positive value (epsilon)) then vectorial field can be recovered to within a global sign with precision C·max((L(delta))^1/4,(check)(epsilon)). Here constants C and D may be explicitly evaluated from the knowing the spectrum of the potential.

The Corollary of the second Result claims uniqueness to within a global sign of recovering the vectorial field from its intensity and location of magnetic equator at the Earth's surface.